Gas turbine blades are generally subjected to variable speeds and loading. The variable loading on the gas turbine blades are mainly caused by fluid jets impacting the gas turbine blades and the starting and shutting down of the gas turbine itself. This variable loading causes variable mean stresses and variable alternating stresses on the gas turbine blades. The variations of these stresses subjects the gas turbine blades to mechanical forces such as fatigue, creep, thermo mechanical fatigue, etc. Fatigue, for example, causes a turbine blade to fail at a stress that is much less than the turbine blade can withstand when it is new.
Many studies have attempted to deal with the problem of turbine blade failure. For example, some studies have attempted to determine the basic fatigue properties of the material of the turbine blade and of the turbine blade design for which the material is being used. Fatigue tests have been conducted in an effort to determine variations in the stress intensity factor over time and to relate these variations to crack nucleation. Some studies have modeled turbine blades as rotating Timoshenko beams with twists and tapers. Also, some studies have addressed damage in such beams using vibration characteristics.
However, these studies typically have addressed damage at a given point in time during the operational history of the turbine blade and have not looked at the effect of damage growth on the vibration characteristics. Turbine blades undergo cyclic loading. This loading is time dependent and causes deterioration of the turbine blades. To avoid catastrophic failures of the turbine blades, the amount of damage as a function of time should also be determined and used to predict the remaining useful life of the turbine blade so that it can be optimally replaced before failure.